Question

How to graph a parabola `y=1/4x^2`?

Answer 1

1. The curve will be curved along the axis which has less power.

Well,if you are concerned with this question, firstly you can write it as `4y= x^2`,

Now as i said earlier the curve will be bent towards that axis which has less power irrespective of the coefficient of x and y .

About this question, you can see that y has less power so the curve will be bent towards y axis.the graph will be as follows,

graph{x^2/4 [-10, 10, -5, 5]}

Here's another method you could use.

You can put different values of x keeping y constant and note the points that you will get; similarly, you can find values of y keeping x constant.

You can plot these points on the graph and the same graph would be in front of you.

Answer 2

Choose x-values, work out the y-values and plot points.
Join them with a smooth curve to obtain the graph.

Explanation:

The first thing is to have some points to plot to be able to find out what the graph will look like.

Draw a table and select some suitable x values.
`x: -4, -3, -2, -1, - 1," " 2," " 3," " 4`

For each x-value, substitute into the equation given and calculate the y-values,

`y: 4," "2.25," " 1," " 0.25," " 0," " 0.25, " " 1, " " 2.25," " 4`

Notice that the `y`-values are all positive and are symmetrical on either side of `0`

Now plotting the points on a set of axes will give the graph of the parabola.
graph{y=1/4x^2 [-9.42, 10.58, -1.64, 8.36]}